1. Field of the Invention
The technical domain of the invention is the exploitation of hydrocarbon fields. More particularly the invention concerns a method of building a reliable simulator able to forecast quantities produced vs. production parameters, in the particular case of mature fields.
2. Description of the Related Art
Mature hydrocarbon fields represent a special challenge both in terms of investment and allocation of human resources, because the net present value of any new investment diminishes with the degree of maturity. Therefore, less and less time and effort can be invested in reservoir studies to support field exploitation. Still, there remain opportunities to improve the production over a so-called “baseline” or “business as usual” behavior of an entire mature field, even with little investment. Past strategic choices in the way to operate the hydrocarbon field have created some heterogeneity in pressure and saturation. These can be drastically revisited and production parameters reshuffled accordingly. With respect to a mature hydrocarbon field, many production avenues have been explored in the past, and a learning process can be applied: reshuffled parameters can be implemented with low risk.
Two prior art approaches are currently known to model the behavior of a hydrocarbon field and to forecast an expected quantity produced in response to a given set of applied production parameters.
A first approach, called “meshed model” or “finite element modeling” parts a reservoir into more than 100,000s of elements (cells, flowlines . . . ), each cell carrying several parameters (permeability, porosity, initial saturation . . . ), and applies physical laws over each of said cells in order to model the behavior of fluids in the hydrocarbon field. In that case the so-called Vapnik-Chervonenkis, VC-dimension h of the space of solutions S, from which the simulator is selected, is very large. Therefore, the available number m of measured data in history data remains comparatively small, even for mature fields, and the ratio h/m appears to be very large compared to 1. As a result of the Vapnik learning theory, which is further mentioned later, the forecast expected risk R is not properly bounded (due to the Φ term), and such a simulator can not be considered to be reliable, even if it presents a very good match with history data. In practice, it is widely recognized that for such meshed models, a good history match does not guarantee a good forecast: there are billions of ways to match the past, leaving large uncertainty on which one provides a good forecast.
A second approach, by contrast, uses over-simplified models, such as, for instance, decline curves or material balance. However, this is too simplified to properly take into account the relevant physics and geology of the reservoir, in particular complex interaction and phenomena. In such case, the forecast expected risk R is not minimized, because no good match can be reached (the empirical Risk Remp term remains large).